結果
| 問題 |
No.1321 塗るめた
|
| コンテスト | |
| ユーザー |
 tko919
|
| 提出日時 | 2020-12-18 00:50:15 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 9,611 bytes |
| コンパイル時間 | 2,475 ms |
| コンパイル使用メモリ | 190,664 KB |
| 実行使用メモリ | 33,128 KB |
| 最終ジャッジ日時 | 2024-09-21 08:45:44 |
| 合計ジャッジ時間 | 10,081 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 42 RE * 3 |
ソースコード
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
//template
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll;
const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
//end
template<unsigned mod=998244353>struct fp {
using uint=unsigned; uint v;
static uint get_mod(){return mod;}
int inv() const{
int tmp,a=v,b=mod,x=1,y=0;
while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);
if(x<0){x+=mod;} return x;
}
fp(ll x=0){init(x%mod+mod);}
fp& init(uint x){v=(x<mod?x:x-mod); return *this;}
fp operator-()const{return fp()-*this;}
fp pow(ll t){fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}
fp& operator+=(const fp& x){return init(v+x.v);}
fp& operator-=(const fp& x){return init(v+mod-x.v);}
fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}
fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}
fp operator+(const fp& x)const{return fp(*this)+=x;}
fp operator-(const fp& x)const{return fp(*this)-=x;}
fp operator*(const fp& x)const{return fp(*this)*=x;}
fp operator/(const fp& x)const{return fp(*this)/=x;}
bool operator==(const fp& x)const{return v==x.v;}
bool operator!=(const fp& x)const{return v!=x.v;}
friend istream& operator>>(istream& is,fp& x){is>>x.v; return is;}
friend ostream& operator<<(ostream& os,fp x){os<<x.v; return os;}
}; using Fp=fp<>;
template<typename T>struct factorial {
vector<T> Fact,Finv,Inv;
factorial(int maxx){
Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx);
Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1;
rep(i,2,maxx){Fact[i]=Fact[i-1]*i;} Finv[maxx-1]=Fact[maxx-1].inv();
for(int i=maxx-1;i>=2;i--){Finv[i-1]=Finv[i]*i; Inv[i]=Finv[i]*Fact[i-1];}
}
T fact(int n,bool inv=0){if(inv)return Finv[n];else return Fact[n];}
T inv(int n){return Inv[n];}
T nPr(int n,int r){if(n<0||n<r||r<0)return Fp(0);else return Fact[n]*Finv[n-r];}
T nCr(int n,int r){if(n<0||n<r||r<0)return Fp(0);else return Fact[n]*Finv[r]*Finv[n-r];}
};
template<typename T=Fp,unsigned p=3>struct NTT{
vector<T> rt,irt;
NTT(int lg=21){
unsigned m=T::get_mod()-1; T prt=p;
rt.resize(lg); irt.resize(lg);
rep(k,0,lg){
rt[k]=-prt.pow(m>>(k+2));
irt[k]=rt[k].inv();
}
}
void ntt(vector<T>& f,bool inv=0){
int n=f.size();
if(inv){
for(int m=1;m<n;m<<=1){ T w=1;
for(int s=0,t=0;s<n;s+=m*2){
for(int i=s,j=s+m;i<s+m;i++,j++){
auto x=f[i],y=f[j];
f[i]=x+y; f[j]=(x-y)*w;
} w*=irt[__builtin_ctz(++t)];
}
} T mul=T(n).inv(); rep(i,0,n)f[i]*=mul;
}else{
for(int m=n;m>>=1;){ T w=1;
for(int s=0,t=0;s<n;s+=m*2){
for(int i=s,j=s+m;i<s+m;i++,j++){
auto x=f[i],y=f[j]*w;
f[i]=x+y; f[j]=x-y;
} w*=rt[__builtin_ctz(++t)];
}
}
}
}
vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0){
if(a.empty() and b.empty())return vector<T>();
int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
vector<T> res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res);
if(same)rep(i,0,m)res[i]*=res[i];
else{
vector<T> c(m); rep(i,0,b.size())c[i]=b[i];
ntt(c); rep(i,0,m)res[i]*=c[i];
} ntt(res,1); return res;
}
};
NTT<Fp,3> ntt;
vector<Fp> mult(const vector<Fp>& a,const vector<Fp>& b,bool same){
return ntt.mult(a,b,same);
}
factorial<Fp> fact(2010101);
template<typename T=Fp>struct Poly:vector<T>{
Poly(int n=0){this->assign(n,T());}
Poly(const vector<T>& f){this->assign(ALL(f));}
T eval(const T& x){T res; for(auto& v:*this)res*=x,res+=v; return res;}
Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;}
void shrink(){while(!this->empty() and this->back()==0)this->pop_back();}
Poly inv()const{
assert(this->front()!=0); const int n=this->size();
Poly res(1); res.front()=T(1)/this->front();
for(int k=1;k<n;k<<=1){
Poly g=res,h=*this; h.resize(k*2); res.resize(k*2);
g=(g.square()*h); g.resize(k*2);
rep(i,k,min(k*2,n))res[i]-=g[i];
}
res.resize(n); return res;
}
Poly square()const{return Poly(mult(*this,*this,1));}
Poly operator+(const Poly& g)const{return Poly(*this)+=g;}
Poly operator-(const Poly& g)const{return Poly(*this)-=g;}
Poly operator*(const Poly& g)const{return Poly(*this)*=g;}
Poly operator/(const Poly& g)const{return Poly(*this)/=g;}
Poly operator%(const Poly& g)const{return Poly(*this)%=g;}
Poly& operator+=(const Poly& g){
if(g.size()>this->size())this->resize(g.size());
rep(i,0,g.size()){(*this)[i]+=g[i];} shrink(); return *this;
}
Poly& operator-=(const Poly& g){
if(g.size()>this->size())this->resize(g.size());
rep(i,0,g.size()){(*this)[i]-=g[i];} shrink(); return *this;
}
Poly& operator*=(const Poly& g){
*this=mult(*this,g,0);
shrink(); return *this;
}
Poly& operator/=(const Poly& g){
if(g.size()>this->size()){
this->clear(); return *this;
}
*this=this->rev(); g=g.rev();
int n=this->size()-g.size()+1;
this->resize(n); g.resize(n);
*this*=g.inv_fast(); this->resize(n); //
*this=this->rev(); shrink(); return *this;
}
Poly& operator%=(Poly& g){*this-=*this/g*g; shrink(); return *this;}
Poly diff()const{
Poly res(this->size()-1);
rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1);
return res;
}
Poly inte()const{
Poly res(this->size()+1);
for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]*fact.inv(i);
return res;
}
Poly log()const{
assert(this->front()==1); const int n=this->size();
Poly res=diff()*inv_fast(); res=res.inte(); //
res.resize(n); return res;
}
Poly exp()const{
assert(this->front()==0); const int n=this->size();
Poly res(1),g(1); res.front()=g.front()=1;
for(int k=1;k<n;k<<=1){
g=(g+g-g.square()*res); g.resize(k);
Poly q=*this; q.resize(k); q=q.diff();
Poly w=(q+g*(res.diff()-res*q)),t=*this;
w.resize(k*2-1); t.resize(k*2);
res=(res+res*(t-w.inte())); res.resize(k*2);
} res.resize(n); return res;
}
Poly shift(const int& c)const{
const int n=this->size();
Poly res=*this,g(n); g[1]=c; g=g.exp();
rep(i,0,n){res[i]*=fact.fact(i);} res=res.rev();
res*=g; res.resize(n); res=res.rev();
rep(i,0,n){res[i]*=fact.fact(i,1);} return res;
}
Poly inv_fast()const{
const int n=this->size();
Poly res(1); res.front()=T(1)/this->front();
for(int k=1;k<n;k<<=1){
Poly f(k*2),g(k*2);
rep(i,0,min(n,k*2))f[i]=(*this)[i];
rep(i,0,k)g[i]=res[i];
ntt.ntt(f); ntt.ntt(g);
rep(i,0,k*2)f[i]*=g[i];
ntt.ntt(f,1);
rep(i,0,k){f[i]=0; f[i+k]=-f[i+k];}
ntt.ntt(f); rep(i,0,k*2)f[i]*=g[i]; ntt.ntt(f,1);
rep(i,0,k)f[i]=res[i];
swap(res,f);
} res.resize(n); return res;
}
Poly exp_fast()const{
const int n=this->size();
if(n==1)return Poly({T(1)});
Poly b(2),c(1),z1,z2(2);
b[0]=c[0]=z2[0]=z2[1]=1; b[1]=(*this)[1];
for(int k=2;k<n;k<<=1){
Poly y=b; y.resize(k*2);
ntt.ntt(y); z1=z2;
Poly z(k);
rep(i,0,k)z[i]=y[i]*z1[i];
ntt.ntt(z,1);
rep(i,0,k>>1)z[i]=0;
ntt.ntt(z);
rep(i,0,k)z[i]*=-z1[i];
ntt.ntt(z,1);
c.insert(c.end(),z.begin()+(k>>1),z.end());
z2=c; z2.resize(k*2);
ntt.ntt(z2);
Poly x=*this; x.resize(k); x=x.diff(); x.resize(k);
ntt.ntt(x);
rep(i,0,k)x[i]*=y[i];
ntt.ntt(x,1);
Poly bb=b.diff();
rep(i,0,k-1)x[i]-=bb[i];
x.resize(k*2);
rep(i,0,k-1){x[k+i]=x[i]; x[i]=0;}
ntt.ntt(x);
rep(i,0,k*2)x[i]*=z2[i];
ntt.ntt(x,1);
x.pop_back(); x=x.inte();
rep(i,k,min(n,k*2))x[i]+=(*this)[i];
rep(i,0,k)x[i]=0;
ntt.ntt(x);
rep(i,0,k*2)x[i]*=y[i];
ntt.ntt(x,1);
b.insert(b.end(),x.begin()+k,x.end());
} b.resize(n); return b;
}
Poly pow(ll t){
int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;
Poly res(n); if(t*k>=n)return res;
n-=t*k; Poly g(n); T c=(*this)[k],ic=T(1)/c;
rep(i,0,n)g[i]=(*this)[i+k]*ic;
g=g.log(); for(auto& x:g)x*=t; g=g.exp_fast(); //
c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;
}
};
Fp nth(Poly<Fp> p,Poly<Fp> q,ll n){
while(n){
Poly<Fp> ref(q),np,nq;
for(int i=1;i<(int)q.size();i+=2)ref[i]*=-1;
p*=ref; q*=ref;
for(int i=n&1;i<(int)p.size();i+=2)np.emplace_back(p[i]);
for(int i=0;i<(int)q.size();i+=2)nq.emplace_back(q[i]);
swap(p,np); swap(q,nq);
n>>=1;
}
return p[0]/q[0];
}
/*
[x^N*y^K] N! * e^{Mx}((e^x-1)y+1)^M
=N!*nCr(M,K)* [x^N] e^{Mx}(e^x-1)^K
*/
int main(){
int n,m,k; cin>>n>>m>>k;
Poly<Fp> f(n+1),g(n+1);
Fp pw=1;
rep(i,0,n+1){
f[i]=pw*fact.fact(i,1);
g[i]=fact.fact(i,1);
pw*=m;
}
g[0]=0;
f*=g.pow(k);
Fp res=fact.fact(n)*fact.nCr(m,k)*f[n];
cout<<res<<endl;
return 0;
}